# Implicit differentiation help again

• A_Munk3y
In summary, implicit differentiation is used to find the derivative of equations where one variable is dependent on another. In the given equations, the process starts by differentiating both sides of the equation with respect to x, using the chain rule when necessary. In the first equation, there is an error in the simplification of the derivative, resulting in an incorrect equation. In the second equation, the derivative is correctly simplified to [6y(y2 -1) + 1]y' = 2x. The next step is to solve for y' by dividing both sides by [6y(y2 -1) + 1].
A_Munk3y
implicit differentiation help :) again!

## Homework Statement

Use implicit differentiation
1) x/(y-x2)=1

and

2) (y2-1)3=x2-y

## The Attempt at a Solution

1) x/(y-x2)=1
=> [(y-x2)(1)-(x)((1*dy/dx)-2x)]/[(y-x)2]2=0
=> y-x2-x(dy/dx)+2x2=[(y-x)2]2

I think I'm going to stop here because I'm pretty sure it's wrong so no reason to keep putting what i got. What am i doing wrong here?2) (y2-1)3=x2-y
=> 3(y2-1)2*(2y(dy/dx) = 2x-(dy/dx)
=> 3(y2-1)2*(2y(dy/dx))+(dy/dx) = 2x

Now here, i know the next step is
(dy/dx)(3(y2-1)2*(2y)+1)=2x

But i have no idea how i should get to this step. How did the dy/dx (the one that comes first) come out and where did the other dy/dx go (it became a 1??)
can anyone explain this to me?

A_Munk3y said:

## Homework Statement

Use implicit differentiation
1) x/(y-x2)=1

and

2) (y2-1)3=x2-y

## The Attempt at a Solution

1) x/(y-x2)=1
=> [(y-x2)(1)-(x)((1*dy/dx)-2x)]/[(y-x)2]2=0
So far, so good.
A_Munk3y said:
=> y-x2-x(dy/dx)+2x2=[(y-x)2]2
Error above. When you multiply 0 by (y - x2)2, you get 0. If you fix this, the resulting equation is fairly easy to solve for y'.
A_Munk3y said:
I think I'm going to stop here because I'm pretty sure it's wrong so no reason to keep putting what i got. What am i doing wrong here?

2) (y2-1)3=x2-y
=> 3(y2-1)2*(2y(dy/dx) = 2x-(dy/dx)
=> 3(y2-1)2*(2y(dy/dx))+(dy/dx) = 2x
This is [6y(y2 -1) + 1]y' = 2x
The next step should be obvious.
A_Munk3y said:
Now here, i know the next step is
(dy/dx)(3(y2-1)2*(2y)+1)=2x

But i have no idea how i should get to this step. How did the dy/dx (the one that comes first) come out and where did the other dy/dx go (it became a 1??)
can anyone explain this to me?

## What is implicit differentiation?

Implicit differentiation is a mathematical technique used to find the derivative of a function when the equation cannot be easily solved for the dependent variable.

## When is implicit differentiation used?

Implicit differentiation is used when the given function is in an implicit form, meaning the dependent variable is not isolated on one side of the equation.

## How do you perform implicit differentiation?

To perform implicit differentiation, you must differentiate both sides of the equation with respect to the independent variable. Then, isolate the derivative of the dependent variable on one side of the equation to solve for it.

## What is the difference between implicit differentiation and explicit differentiation?

Explicit differentiation is used when the given function is in an explicit form, meaning the dependent variable is already isolated on one side of the equation. Implicit differentiation, on the other hand, is used when the given function is in an implicit form.

## What are some common mistakes when using implicit differentiation?

Some common mistakes when using implicit differentiation include forgetting to use the chain rule, not differentiating all terms in the equation, and incorrectly isolating the derivative of the dependent variable. It is important to carefully follow the steps and double check your work to avoid these mistakes.

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